Independent Definition and 713 Threads

Hello. I'm trying to understand why P(A|B) ≠ (PA) given that the events are indepent is this case. I am not sure if my working out is correct but the answer is 1/8 in the answer section. Events A and B are defined in the sample space S. The events A and B are independent. P(A) = 0.3, P(B) =...

Hello, I was wondering if anyone had any good ideas on a topic or course that I could take next Fall as an independent study? I will be taking Number Theory this summer and Real Analysis, Abstract Algebra and either Numerical Analysis or Complex Analysis next Fall.I spoke to one of my...

Has anyone heard of an independent study for freshman/sophomore students for physics/engineering majors? What are your perspectives on it? Is it too early? Or is it a good to have? I ask because I spoke to one of the faculty members about it-- and he replied that it is too early. He wasn't...

question in attachment. please help!

Homework Statement Hello! I am currently stuck with a time independent Schrodinger equation where the potential "V(x)" is hyperbolic in nature. I was wondering if anyone could give me a hint as to how I should approach this problem in order to get an analytical solution (without using...

Homework Statement So, I know the pdf for independent random variables is found by using the convolution; the pdf is f[sub:X+Y](a) = ∫ f[sub:X](a-y)f[sub:Y](y)dy, but can I just use the density function for a function of a random variable instead; that is: f[sub:X+Y](x[u,v], y[u,v])(Jacobian...

There are four basic equations for constant acceleration v = v_o +at v^2 = v_o^2 +2as and so on The first velocity is time dependent, while the second velocity relationship is time independent. In varying acceleration, we have v = ∫ a(t) dt Is there any other way we can define...

Homework Statement let x_{i} be a random variable, and let y_{j} = \sum x_{i}. The variance of the random distribution of the x_{i}'s is known, and each y is the sum of an equal amount of x_{i}'s, say N of them. How do I compute the variance of y in terms of \sigma^2_{x} and N? Homework...

Homework Statement Let S be a linearly independent subset of a Hilbert space. Prove that span(S) is a subspace, that is a linear manifold and a closed set, if and only if S is finite. Homework Equations The Attempt at a Solution Assuming S is finite means that S is a closed set...

Homework Statement Determine which of the following pairs of functions are linearly independent. (a) f(t)=3t,g(t)=|t| (b) f(x)=x^{2},g(x)=4|x|^{2} Homework Equations the Wronskian is defined as, W=Det{{f(u),g(u)},{f'(u),g'(u)}} if {f(u),g(u)} are linearly dependent, W=0...

So I have a question for you guys - what do you do if your test grades don't seem to be affected by how much you've studied? Here's the short version of my problem: Study a bit = ~85 and 2 out of 3 times so far, the highest grade. Don't study at all and get one hour of sleep = 80 (the...

Homework Statement Show that if {a, b, c} is a linearly independent set of vectors, then so are {a, b}, {a, c}, {b, c}, {a}, {b}, and {c}. Homework Equations None. The Attempt at a Solution Well I was just thinking that if {a, b, c} is a linearly independent set of vectors, then...

Homework Statement This was a question on my lecture slides which I didn't quite understand during the lecture. Here is the circuit: http://img843.imageshack.us/img843/3548/nodesbranchesloops.jpg The question was to find independent loops in the circuit. On the left-hand side I drew in the...

Given the fact that X and Y are independent Cauchy random variables, I want to show that Z = X+Y is also a Cauchy random variable. I am given that X and Y are independent and identically distributed (both Cauchy), with density function f(x) = 1/(∏(1+x2)) . I also use the fact the...

I have: $Z=X_1+\ldots+X_N$, where: $X_i\sim_{iid}\,\text{Exponential}(\lambda)$ $N\sim\,\text{Geometric}_1(p)$ For all $i,\,N$ and $X_i$ are independent. I need to find the probability distribution of $Z$: $G_N(t)=\frac{(1-p)t}{1-pt}$ $M_X(t)=\frac{\lambda}{\lambda-t}$...

Lets say I roll 2 dice. We have 36 possible elementary events. I want to know what is the probability that I rolled an even number, given that I rolled both same dice. So my event A={<1,1>, <2,2>, <3,3>, <4,4>, <5,5>, <6,6>} My event B={<2,2>, <4,4>,<6,6>} Conditional probability is...

Homework Statement The n random variables X_{1}, X_{2},..., X_{n} are mutually independent and distributed with the probability density f(x)=\frac{1}{\pi(1+x^{2})} i) Find the probability density of the average Y=\frac{1}{n}\Sigma^{i=1}_{n}X_{i} ii) Explain why it does not converge...

hallo I am trying to calculate the probability to obtain 2 sets of linearly independent vectors from a set of binary vectors of length k. For example: k = 4, and therefore I have 2^k = 16 vectors to select from. I want to randomly select 7 vectors (no repetition). What is the...

Homework Statement During a winter season at one ski resort, there are two roads from Area A to Area B and two roads from Area B to Area C. Each of the four roads is blocked by snow with a probability p=.25 independently of the other roads. What is the probability that there exists an open...

Hello! I am trying to understand an example from my book that deals with two independent Poisson random variables X1 and X2 with parameters λ1 and λ2. The problem is to find the probability distribution of Y = X1 + X2. I am aware this can be done with the moment-generating function technique...

I was wondering why when we derive the euler lagrange equations and when we use them we treat x and x dot as independent quantities?

Bag contains 9 blue balls, 3 red balls. A ball is selected at random, colour recorded and NOT replaced. A second ball is selected at random, colour recorded. a) Draw tree diagram (no problem). Part 2 a) Find probability second ball is red (no problem, 0.25) b) Find probability both...

Hi all, I got stuck with the following problem: Let X, Y and Z be three random vectors of the same length drawn from a continuous random distribution. where Z is independent of X and Y but Y=f(X) with a non-linear function f. Can I claim that: 1. Z^{T}X\neq 0 almost surely...

Homework Statement Theres two current sources and three voltages sources the problem wants to know the power supplied by each current source Homework Equations according to the book the problem can be solved using Kirchoffs current law and kirchhoffs voltage law The answers according...

Hi all, this thread is mainly aimed at postgrads. I'm doing my undergrad degree in theoretical physics, my question is this; how many hours of independent study did you do while an undergrad? I've been getting good scores so far, but have only been averaging about an hour a day outside contact...

In general 4d space time, the Riemann tensor has 20 independent components. However, in a more symmetric metric, does the number of independent components reduce? Specifically, for the Schwartzchild metric, how many IC does the corresponding Riemann tensor have? (I think it is 4, but I...

Hi. Why in all literature bus arrivals are referred as independent random variables (Poisson as well)? Is there any reference where there is some math explanation except intuitive approach which of course tell that there is no correlation between 2 bus arrivals? Best regards

Homework Statement Let U be the subspace of R5 spanned by the vectors E={(1,1,0,0,1),(1,1,0,1,1),(0,1,1,1,1),(2,1,-1,0,1)}. Find a linearly independent subset F of E with Span(E)=U Homework Equations The Attempt at a Solution I figured out that E is linearly dependent and that...

Hello. My question is directed to those of you who actually have some experience in the area or who can provide detailed information rather than general/theoretical guidance. I would like to ask you about funding sources available for an independent scientist on the U.S. or international...

i'm an undergrad in stats, and next semester is my last. I'm doing an independent study next semester, and am unsure of what would be more beneficial for me: a class in R, or bayes. i would like to do bayes, and I'm decent on computers with limited programming experience, so I'm not too worried...

Hello, I've been studying some linear algebra, and i am stuck on a certain definition. The book i am using says that points{p0,p1,...,pk} in a vector space V are barycentrically independent if and only if the vectors {p1-p0,p2-p0,...,pk-p0} are linearly independent. The problem i have is the...

Homework Statement Find a collection of well-formed formulas Ʃ such that Ʃ has no independent equivalent subset. Homework Equations N/A The Attempt at a Solution So far I have been able to show that Ʃ must be infinite. However, after this, I get stuck. Could anyone give me a hint...

Hi, I'm looking for suggestions on what are the best areas of theoretical physics for independent/amateur research? I want to do some independent study with a view to research, but my problem is that I can get interested in more-or-less anything and am easily sidetracked. So I want to try to...

Hey everyone! Unfortunately, I made myself a great mistake by taking a course in Ethics over the summer, and I felt as if I hardly learned anything at all because the course was paced too quickly for me to handle, which is why I passed it with a "C." I wanted to see if I could possibly...

In differential geometry, how can one show that the area form: √(EG-F2)du\wedgedv is independent of the choice of local parameterization? Here E,F,G are the coefficients of first fundamental form. Please someone gives me some ideas.

I have always had a passing interest in physics, but would like to strengthen my knowledge of physics. I am looking for a good sequence of topics to begin my studies and work through physics content. I had a basic physics course in college, but would probably need to refresh my knowledge. So...

in particular, i wonder if the trasposition super operator is basis independent or not. We can always write an operator W as \hat{W}=\sum_{i,j} c_{i,j} |i\rangle\langle j| and for the transposed we obtain \hat{W}^T=\sum_{i,j} c_{j,i} |i\rangle\langle j| we obtain a relation true for each...

1. When crossing over does not occur, how many possible chromosome combination can result from independent assortment of the homologous chromosomes? I believe it is 4, because we have 4 identical chromosomes. Is this correct? 2. How does this change when crossing over occurs? It increases or...

Are there any inctances where by examing the trajectory where a subatom went are there experiments where wave functions collapse independently of an observer? Also I was wondering if wave functions collapse naturlley in the universe when they collide into other subatoms or such things. A...

Homework Statement Suppose that S={u,v,w} is a basis of R3. a) Is {u-v,u+v} linearly independent? Why or why not? b) Does {u+v,u-v} span R3? Why or why not? Homework Equations na The Attempt at a Solution a) Because we know that u,v,w are linearly independent and span R3...

Homework Statement Suppose X1 , X2 , . . . , Xn are independent random variables, with common expectation μ and variance σ^2 . Let Sn = X1 + X2 + · · · + Xn . Find the variance of Sn. The attempt at a solution Expected value: E[S_n] = n E[X_i] = n\mu \hspace{10 cm} (1)...

Homework Statement Given the this circuit calculate the voltage through the 3amp source? attached is a jpeg of the circuit. I wasn't able to get a good score on this one question quiz since this boggled me. Is true if I put current source that it will dictate the current of the battery...

"Construct a sample space to show that the truth of this statement P(A\bigcapB\bigcapC)=P(A)*P(B)*P(C) is not enough for the events A,B,C to be mutually independent. Hint: Try finite sample spaces with equally likely simple events." So, my though is that I need to find a sample space with...

Homework Statement Let F be a subset of the complex numbers. Let V be a vector space over F, and suppose α, β and γ are linearly independent vectors in V. Prove that (α+β), (β+γ) and (γ+α) are linearly independent. Homework Equations None. The Attempt at a Solution None. Thanks for your time.

I have done well in undergraduate mathematics, and would like to do some self study in something more advanced and stimulating. I am interested in concepts such as number theory and set theory, or any type of mathematics that can be used to study systems of information, behavior...anything...

Homework Statement "In each of the given cases, decide whether the specified elements of the given vector space V (i) are linearly independent, (ii) span V, and (iii) form a basis. Show all reasoning. V is the space of all infinite sequences (a0, a1, a2, ...) of real numbers v1 =...

Because of the kinetic energy and frames of reference thread: https://www.physicsforums.com/showthread.php?t=534883 I was wondering how to show that a change from potential to kinetic energy in a closed system is independent of the (inertial) frame of reference. I think the math below...

The definition of independence of random variables from a measure-theoretic standpoint is so confusing (independence of generated sigma-algebras, etc.) that I cannot answer this seemingly simple question...So if X,Y are independent random variables, does that mean X,X^2,X^3,X^4,\ldots and...

I need to publish a list of a committee members. Is there any better way of preceding each persons name by Mr/Ms ? Like 1. Mr/Ms Rajendra Adhikari ---- Chairman 2. Mr/Ms Ramkumar kafle ----- Vice-Chairman . . etc. I am searching for single word replacement for Mr/Ms if there is any?

Show that an event A is independent of every event B if P(A)=0 or P(A)=1. **I was able to prove the first part of this problem that is that the events are independent when P(A)=0. However I am stuck on the part where P(A)=1. I have this so far: P(A n B) = P(A)P(B/A) =...